Question: Simplify the following expression: $q = \dfrac{y^2 + 12y + 27}{y + 3} $
Solution: First factor the polynomial in the numerator. $ y^2 + 12y + 27 = (y + 3)(y + 9) $ So we can rewrite the expression as: $q = \dfrac{(y + 3)(y + 9)}{y + 3} $ We can divide the numerator and denominator by $(y + 3)$ on condition that $y \neq -3$ Therefore $q = y + 9; y \neq -3$